Create a Brownian Motion Tibble
Usage
brownian_motion(
.num_walks = 25,
.n = 100,
.delta_time = 1,
.initial_value = 0,
.dimensions = 1
)Value
A tibble containing the generated random walks with columns depending on the number of dimensions:
walk_number: Factor representing the walk number.step_number: Step index.y: If.dimensions = 1, the value of the walk at each step.x,y: If.dimensions = 2, the values of the walk in two dimensions.x,y,z: If.dimensions = 3, the values of the walk in three dimensions.
The following are also returned based upon how many dimensions there are and could be any of x, y and or z:
cum_sum: Cumulative sum ofdplyr::all_of(.dimensions).cum_prod: Cumulative product ofdplyr::all_of(.dimensions).cum_min: Cumulative minimum ofdplyr::all_of(.dimensions).cum_max: Cumulative maximum ofdplyr::all_of(.dimensions).cum_mean: Cumulative mean ofdplyr::all_of(.dimensions).
Details
Brownian Motion, also known as the Wiener process, is a continuous-time random process that describes the random movement of particles suspended in a fluid. It is named after the physicist Robert Brown, who first described the phenomenon in 1827.
The equation for Brownian Motion can be represented as:
Where W(t) is the Brownian motion at time t, W(0) is the initial value of the Brownian motion, sqrt(t) is the square root of time, and Z is a standard normal random variable.
Brownian Motion has numerous applications, including modeling stock prices in financial markets, modeling particle movement in fluids, and modeling random walk processes in general. It is a useful tool in probability theory and statistical analysis.
See also
Other Generator Functions:
custom_walk(),
discrete_walk(),
geometric_brownian_motion(),
random_beta_walk(),
random_binomial_walk(),
random_cauchy_walk(),
random_chisquared_walk(),
random_displacement_walk(),
random_exponential_walk(),
random_f_walk(),
random_gamma_walk(),
random_geometric_walk(),
random_hypergeometric_walk(),
random_logistic_walk(),
random_lognormal_walk(),
random_multinomial_walk(),
random_negbinomial_walk(),
random_normal_drift_walk(),
random_normal_walk(),
random_poisson_walk(),
random_smirnov_walk(),
random_t_walk(),
random_uniform_walk(),
random_weibull_walk(),
random_wilcox_walk(),
random_wilcoxon_sr_walk()
Other Continuous Distribution:
geometric_brownian_motion(),
random_beta_walk(),
random_cauchy_walk(),
random_chisquared_walk(),
random_exponential_walk(),
random_f_walk(),
random_gamma_walk(),
random_logistic_walk(),
random_lognormal_walk(),
random_normal_drift_walk(),
random_normal_walk(),
random_t_walk(),
random_uniform_walk(),
random_weibull_walk()
Examples
set.seed(123)
brownian_motion()
#> # A tibble: 2,500 × 8
#> walk_number step_number y cum_sum_y cum_prod_y cum_min_y cum_max_y
#> <fct> <int> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 1 -0.560 -0.560 0 -0.560 -0.560
#> 2 1 2 -0.230 -0.791 0 -0.560 -0.230
#> 3 1 3 1.56 0.768 0 -0.560 1.56
#> 4 1 4 0.0705 0.839 0 -0.560 1.56
#> 5 1 5 0.129 0.968 0 -0.560 1.56
#> 6 1 6 1.72 2.68 0 -0.560 1.72
#> 7 1 7 0.461 3.14 0 -0.560 1.72
#> 8 1 8 -1.27 1.88 0 -1.27 1.72
#> 9 1 9 -0.687 1.19 0 -1.27 1.72
#> 10 1 10 -0.446 0.746 0 -1.27 1.72
#> # ℹ 2,490 more rows
#> # ℹ 1 more variable: cum_mean_y <dbl>
set.seed(123)
brownian_motion(.dimensions = 3) |>
head() |>
t()
#> [,1] [,2] [,3] [,4]
#> walk_number "1" "1" "1" "1"
#> step_number "1" "2" "3" "4"
#> x "-0.56047565" "-0.23017749" " 1.55870831" " 0.07050839"
#> y "-0.71040656" " 0.25688371" "-0.24669188" "-0.34754260"
#> z " 2.1988103" " 1.3124130" "-0.2651451" " 0.5431941"
#> cum_sum_x "-0.5604756" "-0.7906531" " 0.7680552" " 0.8385636"
#> cum_sum_y "-0.7104066" "-0.4535229" "-0.7002147" "-1.0477573"
#> cum_sum_z "2.198810" "3.511223" "3.246078" "3.789272"
#> cum_prod_x "0" "0" "0" "0"
#> cum_prod_y "0" "0" "0" "0"
#> cum_prod_z "0" "0" "0" "0"
#> cum_min_x "-0.5604756" "-0.5604756" "-0.5604756" "-0.5604756"
#> cum_min_y "-0.7104066" "-0.7104066" "-0.7104066" "-0.7104066"
#> cum_min_z " 2.1988103" " 1.3124130" "-0.2651451" "-0.2651451"
#> cum_max_x "-0.5604756" "-0.2301775" " 1.5587083" " 1.5587083"
#> cum_max_y "-0.7104066" " 0.2568837" " 0.2568837" " 0.2568837"
#> cum_max_z "2.19881" "2.19881" "2.19881" "2.19881"
#> cum_mean_x "-0.5604756" "-0.3953266" " 0.2560184" " 0.2096409"
#> cum_mean_y "-0.7104066" "-0.2267614" "-0.2334049" "-0.2619393"
#> cum_mean_z "2.1988103" "1.7556117" "1.0820261" "0.9473181"
#> [,5] [,6]
#> walk_number "1" "1"
#> step_number "5" "6"
#> x " 0.12928774" " 1.71506499"
#> y "-0.95161857" "-0.04502772"
#> z "-0.4143399" "-0.4762469"
#> cum_sum_x " 0.9678513" " 2.6829163"
#> cum_sum_y "-1.9993759" "-2.0444036"
#> cum_sum_z "3.374932" "2.898685"
#> cum_prod_x "0" "0"
#> cum_prod_y "0" "0"
#> cum_prod_z "0" "0"
#> cum_min_x "-0.5604756" "-0.5604756"
#> cum_min_y "-0.9516186" "-0.9516186"
#> cum_min_z "-0.4143399" "-0.4762469"
#> cum_max_x " 1.5587083" " 1.7150650"
#> cum_max_y " 0.2568837" " 0.2568837"
#> cum_max_z "2.19881" "2.19881"
#> cum_mean_x " 0.1935703" " 0.4471527"
#> cum_mean_y "-0.3998752" "-0.3407339"
#> cum_mean_z "0.6749865" "0.4831142"